Population Density and Legislator Voting Behavior in Oklahoma

Introduction

Oklahoma politicos have long assumed the existence of a divide between urban and rural legislators in state politics. The failures of many bills — including SB1647 — have been attributed to this divide, and its alleged influence informs much of the punditry around politics in the state. Despite its influence, no one to my knowledge has empirically evaluated the relationship between district population density and legislator voting behavior or its effects on policy.

In this analysis, I suggest that limited evidence does, in fact, exist in support of the urban-rural divide hypothesis, and that, when bills are likely to disproportionantly effect rural areas, my suggested “urban-rural scores” have at least as much impact on legislator vote choice as more traditional legislator partisan scores.

An Introduction to Factionalism and What it Means for Oklahoma

Oklahoma is thoroughly dominated by the Republican Party. Republican candidates win most local and county elections, hold all 7 of the state’s constitutional offices, and biennially win super majorities in both chambers of the State Legislature. The Democrats elected to the state legislator remain active in writing, sponsoring, and debating legislation, but their coalition is unable to meaningfully impact the success or failure of any bill without substantial Republican cooperation.

Obviously, conflict still exists in the State Legislature, though. What can explain conflict and disagreement between members of the same party? Political scientists attribute the competition and disagreement within majority parties (like Oklahoma Republicans) to the formation of “factions,” or coalitions within the dominant party. It has long been said that the one main factional divide within the Oklahoma State Legislature is between the urban and suburban Republicans and the rural Republicans, but to my knowledge, this has never been empirically evaluated.

In this analysis, I sought to investigate the existence of the “urban-rural divide” within the Oklahoma Republican Party and estimate the effects of population density on legislator partisanship, as well as on roll call voting behavior on SB1647 (a particularly controversial bill said to have been voted on along urban-rural lines).

Demographics of Oklahoma

Oklahoma is not a particularly diverse state in any sense. It is mostly white, mostly working class, mostly conservative, and mostly rural. The visualizations that follow are meant to represent this lack of diversity.

The first set of visualizations shown are interactive maps of the partisan scores in the house and senate districts from the 2022 regular session and PDF plots showing the distribution of those same partisan scores:

The partisan scores (shown in the above maps and PDF plots) used in this project were estimated using the NOMINATE method (Poole and Rosenthal). The scores range from most liberal at “-1” to most conservative at “1.”

NOMINATE scores are the traditional measure of legislator partisanship used in the study of Congress. I have selected a one-dimensional version of NOMINATE for this analysis for simplicity.

A very important consideration here is that NOMINATE scores are generated from legislator voting behavior. They are not objective measures of partisanship that can be compared between chambers - they are only useful within the chamber they were calculated on. The house and senate scores generated in this analysis are more comparable than the Oklahoma house scores and theoretical Texas house scores because the house and senate in Oklahoma vote on many of the same (or similar) bills, but they were generated independently of one another in the data collection phase of this analysis and thus should not be seen as directly comparable scores.

It can be seen in the above PDF plots that partisanship is somewhat close to normally distributed in the house, but is highly right-skewed in the senate. This has implications for the model of vote choice on SB1647 because of the suggestion that partisan score has less to do with vote choice in the senate.

All analysis from hereon out includes district demographic values for Republican legislators only because factionalism within the Republican Party is the subject of this inquiry.

The final set of visualizations are histograms highlighting the distribution of population density in Oklahoma (only including Republican districts):

As can be seen in these histograms, most of Oklahomans live in very rural areas, with the share of people living in each population density decile decreasing as population density increases.

Because population density is extremely right-skewed, I suggest applying a log transformation to the population density values. I also suggest that the hypothesized relationship between population density and partisan score would, in theory, be subject to diminishing marginal returns from population increases because gaps in resources like access to stores, restaurants, and utilities are wider at the lower end of the population density scale. For example, the difference in access to material resources between Medicine Park and Tulsa is far greater than the difference in access between Tulsa and Oklahoma City.

To account for both right-skewness and diminishing marginal returns to population increases, population density has been placed on a logarithmic scale for the rest of this analysis and will be referred to as the “urban-rural score.”

Modeling the Relationship Between Population Density and Partisan Scores

To evaluate the relationship between population density and legislator partisan scores, analysis beyond simple observational statistics is warranted.

This pair of charts serve as an exploratory data analysis phase before the relationship is formally modeled:

These scatterplots do not show a particularly strong relationship between population density and partisan score, but a relationship might still exist.

To mathematically test for a relationship, I have created formal models using ordinary least squares regression. These models also include the following four predictor variables: the fraction of the district that is white, the fraction of the district that is male, the fraction of the district with a college degree, and the fraction of the district below the poverty line. Both the house and senate republican party models can be seen below:

## 
## House Demographics Linear Model
## ==============================================================
##                                        Dependent variable:    
##                                    ---------------------------
##                                          Partisan Score       
## --------------------------------------------------------------
## % With College Degree                        -0.586           
##                                              (0.436)          
##                                                               
## % Male                                       -0.091           
##                                              (1.407)          
##                                                               
## % Below Poverty Line                         -0.165           
##                                              (0.688)          
##                                                               
## % White                                      -0.198           
##                                              (0.260)          
##                                                               
## Population Density (per 0.001 sqm)            0.011           
##                                              (0.009)          
##                                                               
## Constant                                      0.909           
##                                              (0.779)          
##                                                               
## --------------------------------------------------------------
## Observations                                   82             
## R2                                            0.064           
## Adjusted R2                                   0.003           
## Residual Std. Error                      0.155 (df = 76)      
## F Statistic                            1.043 (df = 5; 76)     
## ==============================================================
## Note:                              *p<0.1; **p<0.05; ***p<0.01

## 
## Senate Demographics Linear Model
## ==============================================================
##                                        Dependent variable:    
##                                    ---------------------------
##                                          Partisan Score       
## --------------------------------------------------------------
## % With College Degree                         0.334           
##                                              (1.190)          
##                                                               
## % Male                                       -3.196           
##                                              (4.304)          
##                                                               
## % Below Poverty Line                          0.162           
##                                              (1.994)          
##                                                               
## % White                                       0.030           
##                                              (0.683)          
##                                                               
## Population Density (per 0.001 sqm)           -0.008           
##                                              (0.023)          
##                                                               
## Constant                                      1.852           
##                                              (2.267)          
##                                                               
## --------------------------------------------------------------
## Observations                                   38             
## R2                                            0.053           
## Adjusted R2                                  -0.095           
## Residual Std. Error                      0.231 (df = 32)      
## F Statistic                            0.359 (df = 5; 32)     
## ==============================================================
## Note:                              *p<0.1; **p<0.05; ***p<0.01

From these models, it can be seen that all 5 of the predictor variables used make for very weak predictors of legislator partisan score. None of the five predictor variables achieve statistical significance in either model, and the R-squared values in both models suggest that they each capture only around 5-6% of the variance present in partisan scores. These models do not present a better framework for understanding partisanship among Republicans, but do suggest that district population density has little to no measurable impact on legislator partisan score.

But is the relationship between district population density and partisan score even relevant to the discussion at hand? Should the urban-rural divide in the state legislature exist, wouldn’t one assume that the two variables could theoretically have nothing to do with each other and still both matter in legislator vote choice? It could be suggested that partisan score and the “urban-rural score” I have sought to model could be independent predictors of vote choice.

The urban-rural divide and SB1647

As mentioned in the last section, theoretically, if the urban-rural divide exists, population density would be more related to specific vote choice than general legislator partisan score.

To test for this, I have created a logistic regression model to estimate the relationship between urban-rural score and vote choice on a specific bill, SB1647. SB1647 is highly suitable for this analysis because of its deep demographic implications. SB1647, or the “voucher bill,” would have allowed Oklahoma families to redirect state funds away from the public schools and towards individual-family accounts for subsidizing private school attendance. Rural Oklahomans argued at the time that this bill would unfairly impact rural schools because of their already limited resources and smaller student bodies. This, again, supports the above assumption that my log-transformed urban-rural score is a more accurate model of Oklahoma politics than the raw population density scores.

While future inquires into this topic should use many more bills in their modeling, I have only used one bill for the sake of model simplicity and brevity of analysis, at the obvious expense of the generalizability of the results.

The model below shows the log-odds of a legislator voting in favor of SB1647 based on their district’s urban-rural score and their own partisan score:

## 
## Logistic Regresson for SB1647 Vote
## =============================================
##                       Dependent variable:    
##                   ---------------------------
##                           SB1647 Vote        
## ---------------------------------------------
## Urban-Rural Score           0.0003           
##                            (0.0003)          
##                                              
## Partisan Score               0.145           
##                             (1.508)          
##                                              
## Constant                    -0.087           
##                             (0.642)          
##                                              
## ---------------------------------------------
## Observations                  38             
## Log Likelihood              -25.646          
## Akaike Inf. Crit.           57.293           
## =============================================
## Note:             *p<0.1; **p<0.05; ***p<0.01

As can be seen from this model, although neither predictor achieves statistical significance, the model suggests that variance in urban-rural score is nearly as predictive as variance legislator partisan score when it comes to legislator vote choice on SB1647.

This evidence, while not conclusive by any means, is highly suggestive of urban-rural scores being highly predictive of voter behavior.

Conclusion

From this analysis, I am comfortable drawing the conclusion that, while urban-rural scores do not impact legislator partisan scores, they do seem to have an impact on the odds a lawmaker will vote for particularly contentious bills. I do not suggest that the evidence presented here is conclusive in the discussion around the urban-rural divide, and I advise caution in how far these results are generalized, but I still argue that these results point to the population density of a legislator’s district playing an important role in their vote choice on bills with a particularly adverse impact on rural areas.

Further study on this topic should seek to model other bills suggested to be particularly contentious between urban and rural Republicans, as well as model bills not at all likely to create conflict among Republicans.